Fitting linear models and reading residuals

Fitting linear models and reading residuals

Use fitted linear models with an explicit distinction between observed and predicted values. This practice introduces residuals, supplied regression output, comparison of squared errors and the limits of extending a model beyond its data.

Questions cover the sign and units of a residual, reconstruction of a missing observation, use of slope and intercept output, selection among candidate fits and recognition of a curved residual pattern. All data are labelled synthetic. No least-squares derivation or proprietary calculator is required; any needed output or calculation rule is supplied.

Prerequisites include linear equations, scatter plots, arithmetic with signed numbers and units. Single-select and multiselect tasks combine conceptual understanding, calculation and interpretation. For multiselect questions, evaluate every statement independently and select the complete supported subset.

The authored bank moves from introductory reasoning to applications and error analysis. Questions remain self-contained because delivery order can vary. Work on paper first, use each explanation to check the method as well as the result, and revisit a prerequisite when the same error recurs. This foundation practice supports later precalculus work without claiming mastery from a score alone.